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Question: Answered & Verified by Expert
The vector equation of the line passing through $\mathrm{P}(1,2,3)$ and $\mathrm{Q}(2,3,4)$ is
MathematicsThree Dimensional GeometryMHT CETMHT CET 2021 (23 Sep Shift 2)
Options:
  • A $(\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(\hat{i}+\hat{j}+\hat{k})$
  • B $(\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(\hat{i}-\hat{j}-\hat{k})$
  • C $(\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(2 \hat{i}+3 \hat{j}+4 \hat{k})$
  • D $(\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(2 \hat{i}+6 \hat{j}+12 \hat{k})$
Solution:
1551 Upvotes Verified Answer
The correct answer is: $(\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(\hat{i}+\hat{j}+\hat{k})$
d.r. of line through PQ are $[(2,-1),(3,-2),(4,-3)]$ i.e. $(1,1,1)$ Hence required equation of line is
$$
(\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(\hat{i}+\hat{j}+\hat{k})
$$

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